document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=274047>Question 274047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Quadratic Functions:<BR>\n" );
document.write( "\"The height of a ball thrown straight upward is measured by the function h(t)=-16t^2+40t, where h(t) is measured in feet and t is time in seconds.\"<BR>\n" );
document.write( "A) Evaluate h(1) and explain what the dependent and independent variables represent.<BR>\n" );
document.write( "B) What is the height of the ball after 2.5 seconds?<BR>\n" );
document.write( "C) When is the ball  at a height of 48 ft.?<BR>\n" );
document.write( "D) When will the ball hit the ground?\r<BR>\n" );
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document.write( "* I have answered the first part of (A), getting a solution of 24. I am not sure what the dependent and independent variables are.<BR>\n" );
document.write( "*I have solved (B) for an answer of 0.<BR>\n" );
document.write( "*For part (C), I am not sure how to go about solving this backwards.<BR>\n" );
document.write( "*For part (D), I can't even begin to know what to do. How should I go about solving for this, do I even have enough information? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200085 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=200085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The height of a ball thrown straight upward is measured by the function h(t)=-16t^2+40t,<BR>\n" );
document.write( " where h(t) is measured in feet and t is time in seconds.\"<BR>\n" );
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document.write( "A) Evaluate h(1) and explain what the dependent and independent variables represent.<BR>\n" );
document.write( "24 ft like you said, the dependent variable is h(t), so called because it's value<BR>\n" );
document.write( "depends on the value of t, t is the independent variable<BR>\n" );
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document.write( "B) What is the height of the ball after 2.5 seconds?<BR>\n" );
document.write( "h(2.5) = -16(2.5^2) + 40(2.5) = 0; (which you got)<BR>\n" );
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document.write( "C) When is the ball at a height of 48 ft.?<BR>\n" );
document.write( "Substitute 48 for h(t), find t<BR>\n" );
document.write( "-16t^2 + 40t = 48<BR>\n" );
document.write( "-16t^2 + 40t - 48 = 0<BR>\n" );
document.write( "Simplify, and change the signs divide by -8, (easier to factor)<BR>\n" );
document.write( "2t^2 - 5t + 6 = 0<BR>\n" );
document.write( "There are not any real solutions for this equation, means it never reaches 48 ft<BR>\n" );
document.write( "the discriminant (25 - 48) is negative<BR>\n" );
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document.write( "D) When will the ball hit the ground? <BR>\n" );
document.write( "you already found that out in (B) when the h(t) = 0 (ground level)<BR>\n" );
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document.write( "A graph of this equation will help here<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+4%2C+-10%2C+50%2C+-16x%5E2%2B40x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+4%2C+-10%2C+50%2C+-16x%5E2%2B40x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that it never gets close to 48 ft, the highest point was 25 ft at 1.25 sec </SPAN>\n" );
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